Abstract: Different collocation iterative schemes have been well studied and widely applied for numerical solution of nonlinear hypersingular integral equations. In this paper we apply Newton method and its modified version to solve the equations obtained by applying a collocation method to a nonlinear hypersingular integral equation of Prandtl's type. The corresponding convergence results are derived in suitable Sobolev spaces. Some numerical tests are also presented.
Newton methods for a class of nonlinear hypersingular integral equations / M. R., Capobianco; Criscuolo, Giuliana; P., Junghanns. - In: NUMERICAL ALGORITHMS. - ISSN 1017-1398. - STAMPA. - 55:(2010), pp. 205-221. (Intervento presentato al convegno Second Dolomites Workshop on Constructive Approximation Theory and Applications (DWCAA09) tenutosi a Alba di Canazei nel 2009) [10.1007/s11075-010-9387-8].
Newton methods for a class of nonlinear hypersingular integral equations
CRISCUOLO, GIULIANA;
2010
Abstract
Abstract: Different collocation iterative schemes have been well studied and widely applied for numerical solution of nonlinear hypersingular integral equations. In this paper we apply Newton method and its modified version to solve the equations obtained by applying a collocation method to a nonlinear hypersingular integral equation of Prandtl's type. The corresponding convergence results are derived in suitable Sobolev spaces. Some numerical tests are also presented.| File | Dimensione | Formato | |
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